I have only seen them inside of summations, Σs*,* but I'm sure they are used elsewhere. They are used like a filter. For instance, if you want to sum weights of butterflies in an insect database you would say "for every insect in X, if it is a butterfly then add it's weight to the sum". When it gets translated into an equation, the part "if its a butterfly" gets turned into a Kronecker delta function where it outputs 1 when it is a butterfly and 0 otherwise. So in some sort of pseudo equation, it might look like y=Σ*_of_i_in_X( Kron_delta( Label(i), "butterfly") * Weight(i) )*
I hope this doesn't muddy the water too much, Cody Smith On Mon, Jun 8, 2020 at 4:00 PM Frank Wimberly <[email protected]> wrote: > OK. The Kronecker delta on a set A is a function or set of ordered > pairs. The arguments of the function are ordered pairs of the elements of > A. The elements of the function are defined by <<x,y>, z> where x and y > are elements of A and z is in {0, 1}. In other words the domain of the > Kronecker delta is the set of ordered pairs of elements of A and it's range > is the set {0, 1} and the function is evaluated as delta(x, x) = 1 for all > x and delta(x, y) = 0 if x != y. > > Is that better? > > I stand by my original post > > > --- > Frank C. Wimberly > 140 Calle Ojo Feliz, > Santa Fe, NM 87505 > > 505 670-9918 > Santa Fe, NM > > On Mon, Jun 8, 2020, 3:33 PM Jon Zingale <[email protected]> wrote: > >> Steve, Tom, >> >> The Kronecker delta (or Dirac delta or indicator function depending on >> context) >> appears in the technical machinery of mathematics and so does not usually >> show >> up meaningfully in the target science of the mathematical theory. The >> delta >> is >> a lot like a projection map (likely dual for those playing at home) in >> that >> it is useful >> for selecting data out of larger data, but not in any magical way. It is >> exactly like >> when we select a column in a Google doc, maybe I move the mouse over to >> the >> column and then click the mouse button. This process is internal to how I >> work with >> the data mechanistically and does not really tell me anything about the >> content. >> Seeming exceptions do arise, like when one is working with expectations in >> probability >> theory, but even these cases just make the process of 'counting' easier. >> The >> reason >> we perhaps wish to use something like the Iverson bracket is so that we >> can >> keep track >> of types. By mapping a truth value to a number, like claiming True to be >> 1, >> we can count >> how many people have their hands raised, say. Many people don't really >> concern >> themselves with these differences and are somehow ok with it when we write >> stuff like >> 3 * True = 3, but they are usually javascript programmers. Knuth advocates >> for the use of the Iverson bracket (see Concrete Mathematics) because >> concerning >> oneself with types often leads to more clear and powerful expressions of >> thought. >> >> Jon >> >> >> >> -- >> Sent from: http://friam.471366.n2.nabble.com/ >> >> - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . >> FRIAM Applied Complexity Group listserv >> Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam >> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> archives: http://friam.471366.n2.nabble.com/ >> FRIAM-COMIC http://friam-comic.blogspot.com/ >> > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC http://friam-comic.blogspot.com/ >
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